Step 1) Solve the first equation for #a#:
#a + 3b = 7#
#a + 3b - color(red)(3b) = 7 - color(red)(3b)#
#a + 0 = 7 - 3b#
#a = 7 - 3b#
Step 2) Substitute #(7 - 3b)# for #a# in the second equation and solve for #b#:
#2a = b - 7# becomes:
#2(7 - 3b) = b - 7#
#(2 * 7) - (2 * 3b) = b - 7#
#14 - 6b = b - 7#
#14 + color(blue)(7) - 6b + color(red)(6b) = b + color(red)(6b) - 7 + color(blue)(7)#
#21 - 0 = 1b + color(red)(6b) - 0#
#21 = (1 + color(red)(6))b#
#21 = 7b#
#21/color(red)(7) = (7b)/color(red)(7)#
#3 = (color(red)(cancel(color(black)(7)))b)/cancel(color(red)(7))#
#3 = b#
#b = 3#
Step 3) Substitute #3# for #b# in the solution to the first equation at the end of Step 1 and calculate #a#:
#a = 7 - 3b# becomes:
#a = 7 - (3 * 3)#
#a = 7 - 9#
#a = -2#
The Solution Is:
#a = -2# and #b = 3#
